I believe that each HDR monitor has its preference to display the 10 bit HDR color and co-related brightness. It depends on the hardware color tuning, but not only impacted by the display capability and GPU processing.

OLED panel uses different rendering way on the black part of the scene versus your asus IPS LCD, and OLED has the capability to display pure black to create unlimited contrast if the scene has pure or nearly pure black parts.
It has nothing to do with the maximum brightness capacity.

It's technically hard to tell if your monitor handle the scene with "right color and brightness" or not because you compared it to a different display/panel (perhaps different brand of dispaly). The comparison is not on the same basis.

A TV might use YUV to handle the video signal, but a PC monitor might use RGB. YUV-to-RGB includes some color conversion as well.

If your asus monitor truly entered the HDR displaying, then I think it was displaying video in HDR mode with its hardware preference and configuration.

Last but not the least, an OLED HDR TV probably has a relatively higher price from the asus HDR monitor, and the price does not only regard the monitor size, brightness capability, etc. but also the OLED panel.